Related papers: Shock equations and jump conditions for the 2D Adj…
Adjoints are used in optimization to speed-up computations, simplify optimality conditions or compute sensitivities. Because time is reversed in adjoint equations with first order time derivatives, boundary conditions and transmission…
The characteristic structure of the two-dimensional adjoint Euler equations is examined. The behavior is similar to that of the original Euler equations, but with the information travelling in the opposite direction. The compatibility…
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with…
Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and…
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…
As more and more multiphysics effects are entering the field of CFD simulations, this raises the question how they can be accurately captured in gradient computations for shape optimization. The latter has been successfully enriched over…
The Green's function approach of Giles and Pierce is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution…
The analytic properties of adjoint solutions are investigated for the two-dimensional (2D) full potential equation. For subcritical flows, the Green's function approach is used to derive the analytic adjoint solution for a cost function…
We obtain the analytic adjoint solution for two-dimensional (2D) incompressible potential flow for a cost function measuring aerodynamic force using the connection of the adjoint approach to Green's functions and also by establishing and…
Shock solutions for multi-temperature Euler equations are inherently ambiguous due to the loss of microscopic physical detail during model reduction and occurrence of non-conservative terms. This paper presents a detailed analytical study…
This paper describes an exact solution to the drag-based adjoint Euler equations in two and three dimensions that is valid for irrotational flows.
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
We consider one-dimensional steady-state balance laws with discontinuous solutions. Giles and Pierce realized that a shock leads to a new term in the adjoint error representation for target functionals.This term disappears if and only if…
Aerodynamic drag can be partially approximated by the entropy flux across fluid domain boundaries with a formula due to Oswatitsch. In this paper, we build the adjoint solution that corresponds to this representation of the drag and…
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and…
Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed and an explanation is provided by comparing a…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
A novel adjoint-based framework oriented to optimal flow control in compressible direct numerical simulations is presented. Also, a new formulation of the adjoint characteristic boundary conditions is introduced, which enhances the…
In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than…